تحلیل ارتعاش آزاد جانبی و محوری سدهای بتنی وزنی بدون اثر مخزن به روش‌ گالرگین

نوع مقاله : مقاله پژوهشی

نویسنده

بهرام نوائی نیا

دانشکده مهندسی عمران دانشگاه صنعتی نوشیروانی بابل.

10.22067/jfcei.2025.89758.1320

چکیده

دراین پژوهش، تحلیل ارتعاش آزاد سدهای بتنی وزنی بدون احتساب اثرمخزن با استفاده از دو نظریه تیر اویلر-برنولی و تیر رایلی با نیمرخ متغیر مورد بررسی قرار گرفته‌ است. برای حل معادلات دیفرانسیل حاکم بر ارتعاش آزاد تیر در فضای فرکانسی از روش گالرکین استفاده شده‌ است. به منظور متناهی شدن انتگرال مانده وزنی، شکل مود نامیرای سازه متناظر با نیمرخ ثابت به‌عنوان توابع قیاسی انتخاب شده است. به-منظور تامین شرط پیوستگی، ماتریس‌های جرم و سختی به‌شکل ضعیف بیان گردیدند که براساس آن دترمینان ماتریس سختی دینامیکی تعیین و به‌کمک آن معادله مشخصه و مقدارهای ویژه به‌دست می‌آیند. برای صحت‌سنجی روش حاضر، پاسخ‌های نهایی با روش‌های تحلیلی مقایسه شده است. پس‌از اطمینان از دقت روش، دو نظریه مورد بررسی در تحلیل ارتعاش آزاد سدهای بتنی وزنی مورد ارزیابی قرار گرفته‌اند. مقایسه نتایج به وضوح نشان می‌دهد که برای بسامدهای بالاتر سدهای بتنی وزنی، استفاده از نظریه اویلر-برنولی باعث خطای قابل توجهی می‌شود و استفاده از نظریه‌ رایلی ضروری است.

کلیدواژه‌ها

سدهای بتنی وزنی

ارتعاش آزاد

نظریه اویلر-برنولی

نظریه رایلی

روش گالرکین

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عنوان مقاله English

Transversely and Axial Free Vibration Analysis of Concrete Gravity Dam without Reservoir effect using Galerkin Method

نویسنده English

Bahram Navayi Neya

Babol Noshirvani University of Technoligy

چکیده English

In this study, transverse and axial free vibration analysis of Concrete Gravity Dams is presented. To achieve ordinary differential equations, the undamped governing partial differential equation of vibration of a tapered cantilever beam, based on Euler-Bernuli and Rayleigh theories are transformed to the frequency domain. Galerkin method is then used to solve the free vibration equation for an arbitrary dam geometry. The restrictions that need to be placed on the admissible functions to avoid the infinite terms in the integrals of equations depend on the order of implied differential operators. The corresponding undamped mode shapes of Euler-Bernoulli and Rayleigh beams, which satisfy essential boundary conditions, are chosen as the admissible functions to expand the trial response of the equation of motion. Validation of results shows an excellent agreement between the Galerkin method and exact solutions in this research. Numerical results of free frequency vibration for different cases based on Rayleigh and Euler-Bernoulli theories show that the frequencies of the dam do not match due to the thickness of dams, especially in higher modes. The predicted values of natural frequencies of the dam based on Rayleigh’s theory are less than the values predicted by Euler-Bernoulli’s theory due to the consideration of rotary inertia effect, which becomes significant in very thin dams.

کلیدواژه‌ها English

Concrete Gravity Dams:

Free Vibration: Euler-Bernoulli Theory

: Rayleigh Theory

: Galerkin Method

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